I have been struggling with a problem, and am seeking help on the topic:

I have two dice, one withafaces and the other withbfaces. Only one success can come from each die, such that the success rates of the dice are1/aand1/b. I want to know the expected number of times I must throw both dice to such that I obtain annnumber of successes.

I know from the means of both the binomial distribution and the negative binomial distribution that I must roll dieaan average ofa*ntimes to getnsuccesses and very similar for dieb, but I can't seem to figure out how to combine the probabilities to get the answer.